CHAPTER TWO

LITERATURE REVIEW

2.0 Introductions

This chapter reviews the study according to various authors.

2.1 The distribution of HIV/AIDS among the children below 15 years

AIDS is a global epidemic which is caused by the virus called human immunodeficiency virus (HIV). It will affect the immune system of the body of human beings. The epidemic was firstly recognized in the year 1980. Since then about 20 million people died and 38 million people are estimated living with HIV in the world (MOH, 2005). The rate of infection of the epidemic is still increasing in many countries of the world and it is distributed unevenly.

It is a major development concern in many countries and is destroying the lives and livelihoods of many people around the world. In spite of increased funding, political commitment and progress in expanding access to HIV treatment, the AIDS epidemic continues against the global response. The epidemic remains extremely dynamic. It is expanding fast and also changing its character as the virus exploits new opportunities for transmission. Hence, the number of people living with HIV/AIDS is growing substantially from year to year.

Since HIV/AIDS was acknowledged as a human being problem, the health researchers have been conducting different research in order to tackle or control the epidemic by developing medicine or vaccine. However, due to the very unique nature of the virus they could not succeed in developing a medicine or vaccine that totally cures or protects from the disease. The antiretroviral medicines which are available currently, at best can diminish the infection rate. i.e they are not able to cure people who are infected by this epidemic. More than this, the price of such medicines has been a major problem especially for developing countries (UNAIDS, 2004).

Almost all countries worldwide are affected by the HIV epidemic. No region of the world has been spared. Although the epidemic is global, there is a remarkable regional variation in its distribution. Some regions are highly affected by the epidemic as compared to other regions. Sub-Saharan Africa (SSA) is one of the hot spots where HIV AIDS is widely spread and it is more hard hit by the consequences of epidemic than other parts of the world.

It is the region where the highest number of victims of HIV/AIDS is found. Among all the people who are infected by diseases all over the world, about 68% (22.5 million) are living in this region (UNAIDS, 2010). According to the United Nation classification of ‘generalized epidemic’ about 90% of the countries which are located in SSA are severely affected by the epidemic. This epidemic has remained the major cause of death in this region. Although the region accounts only for 10% of the world population, it comprises almost 25.8 million of the victims of HIV/AIDS in the world. In 2005 an estimated 3.2 million people in the region became newly infected, while 2.4 million died of AIDS. Among the younger generation (15- 24 years) the percentage of HIV infected women and men account for 4.6% and 1.7%, respectively (UNAIDS, 2005). There were 2.7 million new HIV infections in 2010. HIV AIDS accounts for about approximately 90% of all infection.

The important role of knowledge in addressing the HIV/AIDS pandemic has been recognised. Knowledge about HIV/AIDS is considered an important step in behaviour change, while misconceptions can prevent individuals from making informed choices and taking appropriate action. A Joint United Nations Programme on AIDS (UNAIDS, 2005) report revealed that countries that had significantly reduced rates of new HIV/AIDS infections were those that typically invested heavily in AIDS education and awareness initiatives. Studies also show that young people who have been exposed to appropriate sex education tend to delay sex or use condoms (UNAIDS, 2003; UNFPA, 2003), contrary to the fear that sex education leads to greater sexual activity or experimentation.

2.2 Forecast HIV/AIDS prevalence for children aged below 15 years in Uganda

THE TRENDS IN HIV INCIDENCE 2010–2013 USING MATHEMATICAL MODELLING

Source: 2013 MOH Spectrum estimates

The graphical representation trends in HIV/AIDS incidence from 2010-2013

Source: 2013 MOH Spectrum estimates

CHAPTER THREE

METHODOLOGY

3.0 Introduction:

This section presents a detailed description on how the study will be carried out and collecting the necessary data for the study. It therefore covers the research design, study area, data sources, data processing, data analysis techniques and anticipated limitations of the study.

3.1 Data processing and Data analysis techniques.

The process of data processing will involve editing in order to check for errors and omissions and coding to reduce the data to a meaningful pattern of responses. Model specification and soft wares employed in the tabulation and processing of the findings will be done in order to prepare data, analyze and compile a research report.

The study will use time series analysis and descriptive statistics will be used to describe the information got from the field this will be inform of graphs and tables

Data Analysis will involve applying statistical techniques on it for easy presentation. It will include the interpretation of research findings in the light of the research questions, and objectives to determine if the results are consistent with those research questions.

3.2 Descriptive analysis.

3.2.1 Time series analysis

By the nature of data which is the time series

The analysis however will concentrate on trend and seasonality of HIV prevalence

Assuming a multiplicative model, then 𝑌𝑡=𝑇𝑡∗𝑆𝑡

Where 𝑌𝑡 is the mortality series, 𝑇𝑡 is Trend and 𝑆𝑡 is the seasons.

This employs ARIMA modeling and it includes the following data exploration techniques.

1. Graphical presentation

This will involve plotting the series 𝑌𝑡 against time t.

1. Non parametric tests for trend

A run is defined as a series of increasing values or a series of decreasing values. The number of increasing, or decreasing, values is the length of the run. In a random data set, the probability that the (i+1)^th value is larger or smaller than the i^th value follows a binomial distribution, which forms the basis of the runs test. Testing procedure

Ho: the HIV prevalence series is stationary

Ha: the HIV prevalence series is non-stationary.

Autoregressive Integrated Moving Average (ARIMA)

This is also known as the Box-Jenkins model. This methodology will be used to forecast the HIV prevalence for children aged below 15 years. The model is based on the assumption that the time series involved are stationary. Stationary will first be checked and if not found, the series will be differenced d times to make it stationary and then the Autoregressive Moving Average (ARMA) (p, q) will be applied. The ARIMA procedure provides a comprehensive set of tools for univariate time series model identification, parameter estimation, and forecasting, and it offers great flexibility in the kinds of ARIMA models that can be analyzed. The ARIMA procedure supports seasonal, subset, and factored ARIMA models; intervention or interrupted time series models; multiple regression analysis with ARMA errors; and rational transfer function models of any complexity. The Box-Jenkins methodology has four steps that will be followed when forecasting HIV prevalence among children as below;

Identification.0 This involves finding out the values of p, d, and q

where;

p is the number of autoregressive terms

d is the number of times the series is differenced

q is the number of moving average terms

The identification here will be done basing on the correlogram plot obtained. Where both autocorrelation and partial correlation cuts of at a certain point, we conclude that the data follows an autoregressive model. The order p, of the ARIMA model is obtained by identifying the number of lags moving in the same direction. In case the series was non stationary, the number of times we difference the series to obtain stationarity is the value of d.

Estimation. This involves estimation of the parameters of the Autoregressive and Moving average terms in the model. The nonlinear estimation will be used.

Diagnostic checking. Having chosen a particular ARIMA model, and having estimated its parameters, we now examine whether the chosen model fits the data reasonably well. The simple

test of the chosen model will be done to see if the residuals estimated from this model are white noise. If they are, we can accept the particular fit and if not, the model will have to be started over.

Forecasting. Exponential smoothing methods will be used for making forecasts. While exponential smoothing methods do not make any assumptions about correlations between successive values of the time series, in some cases you can make a better predictive model by taking correlations in the data into account. Autoregressive Integrated Moving Average (ARIMA) models include an explicit statistical model for the irregular component of a time series that allows for non-zero autocorrelations in the irregular component.

The forecast for the year 2016 will be done by regressing HIV prevalence against time